If the quadratic equation x^2 + 6x + k = 0 has roots -2 and -4, what is the valu

If the quadratic equation x^2 + 6x + k = 0 has roots -2 and -4, what is the value of k?

If the quadratic equation x^2 + 6x + k = 0 has roots -2 and -4, what is the value of k?

Step 1: Understand that the roots of the quadratic equation are the values of x that make the equation equal to zero.
Step 2: Identify the given roots, which are -2 and -4.
Step 3: Recall Vieta's formulas, which state that for a quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots (r1 + r2) is equal to -b/a and the product of the roots (r1 * r2) is equal to c/a.
Step 4: Since the equation is x^2 + 6x + k = 0, we can see that a = 1, b = 6, and c = k.
Step 5: Calculate the product of the roots: (-2) * (-4) = 8.
Step 6: According to Vieta's formulas, the product of the roots is equal to c/a, which means k = 8 (since a = 1).
Step 7: Conclude that the value of k is 8.

Quadratic Equations – Understanding the standard form of a quadratic equation and how to find roots.
Vieta's Formulas – Using Vieta's relations to relate the coefficients of a polynomial to sums and products of its roots.